Last year Uli Dahmen and his colleagues were studying the behavior of
very small inclusions of lead in a matrix of aluminum, using the Analytical
Electron Microscope at the National Center for Electron Microscopy (NCEM),
which allows the sample's temperature to be varied while it is being imaged.
They watched the behavior of different sizes of particles as they turned
up the heat. Dahmen, a member of Berkeley Lab's Materials Sciences Division
and head of NCEM, says that what they saw when the temperature rose above
423 degrees Celsius came as a big surprise.

Leapin' blobs o' lead! Nanoscale particles
of molten lead inside solid aluminum move just as described by Albert
Einstein in his classic 1905 paper on Brownian motion. The much larger
faceted inclusion at upper right is also molten, but is confined by
the solid matrix.
(Click
here for QuickTime version. Click
here for Windows .avi version.)

"We knew that really small particles of lead in aluminum -- particles
only a few nanometers wide -- superheat enormously before they melt,"
says Dahmen, explaining that while lead in bulk melts at 327 degrees Celsius,
a five-nanometer inclusion can get 100 degrees hotter before it melts.
"But when they do melt, they jump at you! They move so fast they
make you blink."

Since bulk aluminum's melting point is 660 degrees Celsius, this frantic
movement of tiny blobs of liquid lead was occurring within a still-solid
aluminum matrix. The startling phenomenon had been seen before by Bjarne
Schmid, who in 1992 was a graduate student of Dahmen's collaborator, Erik
Johnson, at the University of Copenhagen. But an adequate analysis of
the particle motion wasn't possible at the time, and Schmid's observation
appeared only in his doctoral dissertation.

Electron microscopes and computers have come a long way in the years
since 1992. The configuration of the Analytical Electron Microscope, whose
operations are supervised by NCEM's Tamara Radetic, allowed Dahmen and
his coworkers to videotape the movement of the liquid particles as they
zipped about. After analyzing the videos with powerful desktop computers,
using image-analysis software created with the help of NCEM's John Turner,
the collaborators confirmed what their eyes had led them to suspect: the
rapid motion of the lead particles was an example of classic "Brownian
motion."

In 1827, using a magnifying glass to examine wildflower pollen grains
in water, the Scottish botanist Robert Brown "observed many of them
very evidently in motion" and soon determined that these motions
were not due to water currents or evaporation but apparently "belonged
to the particle itself." At first attributing the activity to life,
he eventually found that any sufficiently small particles, even particles
of ground-up rock or glass, moved in the same way -- and kept on doing
so ad infinitum.

In 1827, using this single-lens microscope,
Scottish botanist Robert Brown first observed what came to be called
Brownian motion among grains of pollen from a North American wildflower,
Clarkia pulchella, suspended in water.

For almost 85 years Brownian motion was argued about but never explained,
until in Albert Einstein's "miraculous year" of 1905 -- the
same year he proposed the special theory of relativity and the quantum
nature of light -- Einstein, who was only distantly acquainted with Brown's
work, published a theory giving precise formulas for predicting the behavior
of small particles of a given size suspended in liquid at a given temperature.

Einstein's explanation, in a nutshell, was that the particles are being
randomly knocked about by collisions with the energetic molecules of the
liquid. The higher the temperature, the faster the molecules move, and
the harder they bump into anything that gets in their way.

"Active Molecules," by the way, are what Brown called his pollen
grains; Einstein's molecules (our modern molecules) are much, much smaller,
although in both cases the meaning is "small mass." The reality
of atoms and molecules was still in dispute when Einstein wrote, and his
paper was intended to suggest a way of confirming their existence as well
as calculating their size.

In the case of nanoscale inclusions of melted lead in aluminum, it's
energetic liquid that's jumping around inside the crystalline structure
of the solid. Nevertheless, by analyzing that movement in their videos,
the researchers determined that Einstein's formulas describe it to a T.

"One measure of random movement, as Einstein described it, is that
when you add up the displacement of the particle in each unit of time,
the mean displacement should be zero," says Dahmen. That is, in Brownian
motion, the magnitude of any bounces in one direction will eventually
be offset by bounces in other directions, true for all directions.

A scatterplot of the motion of a molten
lead particle in solid aluminum shows that the distance and direction
of each displacement, measured at intervals of one-thirtieth of a
second, are randomly distributed about the graph's origin.

Another way to test whether a particle's motion is Brownian is to determine
its fractal (or fractional) dimension. A jagged curve on a plane, for
example, which is neither a smooth, one-dimensional line nor a two-dimensional
surface, will have a fractal "dimension" somewhere between 1
and 2.

Brownian motion in the plane is peculiar in that its fractal dimension
is 1.5, exactly halfway between a one-dimensional line and a two-dimensional
plane. The direction and distance of each step in the particle's "drunkard's
walk" is random and unpredictable; for it to get from one exact point
to another would thus take virtually forever, and the curve marked out
by all the steps would fill the plane. (Like considerations apply to Brownian
motion in one or three dimensions.)

The trajectory of a molten lead particle
in solid aluminum at 438°C, determined from 1,056 video frames.

To allow trajectories to be tracked and accurate statistics of frame-by-frame
movement to be compiled, NCEM's image-analysis software had to "grab"
every frame of a thousand frames of video, follow the center of mass of
specific particles, and correct for drift of the image -- a process requiring
the acquisition of several thousand data points per frame, which even
on a fast computer consumed hours. "In principle this could be done
by hand, but it would take forever, and the accuracy would be lousy,"
Dahmen says.

The confirmation that Einstein's theory of Brownian motion applied in
most circumstances had important implications for the study of alloys.
Einstein's theory allows one to calculate the rate of diffusion of a Brownian
particle through the surrounding medium, knowing only its size, the temperature,
and the mechanism of an elementary step through the crystalline solid.

"This may allow us to determine diffusion constants for different
alloys by observing the behavior of individual particles," says Dahmen.
"By recording particles of known size at, say, five different temperatures,
we can calculate the activation energy of the diffusion process."

Having confirmed the Brownian character of the particle motion they first
observed, the researchers also noted circumstances when it was definitely
not random. "These are the most interesting," Dahmen says. For
example, "in some cases there is interaction -- the particles 'talk'
to each other." Particles of some sizes seem to travel as a group,
while smaller particles (though rarely) even seem to repel one another.

Why do some particles coalesce and others keep their distance? Promising
ideas are under investigation, but at this point "I wonder too,"
Dahmen laughs.

"Our discovery of the Brownian motion came as an outgrowth of our
studies of 'magic sizes,'" Dahmen notes, a phenomenon he and Erik
Johnson and their coworkers described in the late 1990s. Nanoscale lead
inclusions in aluminum occur only in some sizes and not in others. (The
two metals were deliberately chosen because they don't readily mix, and
they melt at quite different temperatures.) Moreover, the regular crystalline
shapes of larger inclusions is lost in smaller ones, whose truncated forms
minimize their energy as they interface with the aluminum; this difference
in crystal shape as well as size has an important influence on their melting
temperature.

It's evident that size differences are important in the way melted particles
move as well, with smaller particles moving much faster. Other behaviors
also vary by discrete sizes, and research to understand these size-dependent
behaviors is ongoing.

A number of exciting questions are still open, including the diffusion
mechanisms by which liquid particles move through a solid matrix, and
nonrandom particle activity near defects or grain boundaries in the matrix.
The exotic nanoscale behaviors of a seemingly unromantic metal alloy have
opened a vista of research possibilities for microscopy.

Says Dahmen, "We have found a zoo of behaviors with a simple binary
system of lead and aluminum."

Notices of this work by U. Dahmen, T. Radetic, J. Turner, S. Prokofyev,
M. T. Levinsen, and E. Johnson appear in Proceedings of the International
Congress on Electron Microscopy-15 and Proceedings: Microscopy
and Microanalysis 2002.